January 2nd, 2014, 07:06 PM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Infinite sets
Please look at the picture and answer the question. For question 36. I tried drawing rays from the center of the circle. This does give a 11 correspondence between the points on the circle and the triangle outside. BUT as the rays travel outside to meet the sides of the triangle they diverge. This causes some points on the triangle to be missed out (no 11 correspondence). For question 37. I tried to draw rays from a point inside the triangle. Again we get a 11 correspondence as required but due to divergence of the rays some points on the circle miss out. 
January 2nd, 2014, 07:53 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Infinite sets
Can you demonstrate a onetoone correspondence between the points of two line segments of differing lengths?

January 2nd, 2014, 08:19 PM  #3  
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Re: Infinite sets Quote:
Where am I going wrong?  
January 2nd, 2014, 08:40 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2205 
It's impossible to identify a point on BC without a partner point on DE.

January 2nd, 2014, 09:17 PM  #5  
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Re: Quote:
 
January 2nd, 2014, 11:22 PM  #6  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Infinite sets Quote:
 
January 3rd, 2014, 05:03 AM  #7  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Infinite sets Quote:
 
January 3rd, 2014, 06:08 AM  #8  
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2205  Quote:
Another example: the arctan function, defined on all the reals, is invertible, so it provides a 11 correspondence between all real numbers and the open interval (?/2, ?/2).  

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